Euler diagrams are used to show set membership for various objects. In an Euler diagram, an object may be a member of two, three, or more sets, while other objects may be a member of only one set. Conventional Euler diagrams use circles, ellipses, and other convex shapes to represent the sets and the members of overlapping sets. Euler diagrams are commonly used for very simple sets with limited numbers of objects because there is a limited number of configurations of overlapping circles to define the sets and intersections between sets. Practical applications of conventional Euler diagrams are usually limited to relatively small diagrams with limited numbers of objects and sets with simple intersections.